Rotational Mechanical Converter (MA)

Interface (converter) between humid air and mechanical rotary networks.

blockType: AcausalFoundation.MoistAir.Elements.RotationalMechanicalConverter

Path in the library:

/Physical Modeling/Fundamental/Moist Air/Elements/Rotational Mechanical Converter (MA)

Description

Block Rotational Mechanical Converter (MA) It is an interface between a humid air network and a mechanical rotary network. The unit converts humid air pressure into mechanical torque and vice versa. It can be used as a base for rotary actuators.

The volume of humid air in the converter changes during operation. The pressure and temperature vary depending on the compressibility and heat capacity of the volume of moist air. Liquid water condenses from the volume of moist air when it reaches saturation.

Parameter Mechanical orientation determines whether an increase in the volume of humid air leads to a positive or negative rotation of port R relative to port C.

Port A is the humid air port corresponding to the input of the converter. Ports R and C are mechanical rotary ports corresponding to the shaft and housing respectively.

Subscript indexes:

— properties of dry air, water vapor, and impurity moist air, respectively;
— water vapor at saturation;
— the appropriate port;
— properties of the internal volume of humid air.

Characteristics of the simulated system:

— mass consumption;
— the rate of energy consumption;
— heat consumption;
— pressure;
— density;
— universal gas constant;
— the volume of moist air inside the converter;
— specific heat capacity at constant volume;
— specific enthalpy;
— specific internal energy;
— mass fraction ( — specific humidity, which is otherwise called the mass fraction of water vapor);
— molar fraction;
— relative humidity;
— humidity coefficient;
— temperature;
— the time.

The net consumption of moist air in the tank is:

where

— condensation rate;
— the rate of condensate energy loss;
— the rate of energy addition from sources of moisture and impurity gases;
and — massive flow of water and air through the port S.

Values and They are determined by sources of moisture and impurity gas connected to the S port of the converter.

If the port is not in use, then the terms of the equation with the subscript corresponding to the port name are equal to .

The conservation of water vapor mass relates the mass flow rate of water vapor to the dynamics of the humidity level in the internal volume of humid air:

Similarly, the conservation of impurity gas mass relates the mass flow rate of impurity gas to the dynamics of the impurity gas level in the internal volume of humid air:

The conservation of the mass of the mixture relates the mass flow rate of the mixture to the dynamics of pressure, temperature, and mass fractions of the internal volume of moist air.:

where — the rate of change in the volume of the converter.

Finally, the law of conservation of energy relates the rate of energy flow to the dynamics of pressure, temperature, and mass fractions of the internal volume of humid air.:

The equation of state relates the density of a mixture to pressure and temperature:

The universal gas constant of the mixture is:

The volume of the converter depends on the rotation of the shaft:

where

— the volume of liquid at which the angle of rotation of the shaft is 0;
— volumetric displacement of the shaft;
— angle of rotation of the shaft;
— coefficient of mechanical orientation. If the parameter Mechanical orientation set to the value Pressure at A causes positive rotation of R relative to C Then , otherwise .

The rotation of the shaft is zero if the volume of moist air inside the converter is equal to . Then, depending on the value of the parameter Mechanical orientation, the following is true:

If it is set to Pressure at A causes positive rotation of R relative to C, then the rotation of the interface increases when the volume of moist air increases compared to the dead volume.
If it is set to Pressure at A causes negative rotation of R relative to C, the rotation of the interface decreases when the volume of moist air increases compared to the dead volume.

The equation describing the equilibrium of torques on the converter:

where

— torque from port R to port C;
— atmospheric pressure.

The gas and thermal resistances in the converter are not modeled:

When the air reaches saturation, moisture condensation may occur. The specific humidity at saturation is:

where

— relative humidity of the air at saturation (usually 1);
— saturation pressure of water vapor, estimated at .

The condensation rate is:

where — parameter value Condensation time constant.

The condensate is subtracted from the volume of humid air, as shown in the conservation equations. The energy associated with the condensate is:

where — the specific enthalpy of vaporization, estimated at .

Other amounts of moisture and impurity gas are related as follows:

Assumptions and limitations

The walls of the transducer are ideally rigid.
The gas resistance between the input and the inside of the converter is negligible.
The thermal resistance between the H port and the volume of humid air is not modeled.
The mobile interface works losslessly.
The block does not simulate such mechanical effects as hard stop, friction and inertia.

Variables

Use the parameter group Initial Targets to set the priority and initial target values for the block parameter variables before modeling. For more information, see Configuring physical blocks using target values.

Ports

Conserving

# C — hull
translational mechanics

Details

Mechanical progressive port, corresponds to the inverter housing.

Program usage name

case_flange

# R — shaft
`rotational mechanics

Details

Mechanical progressive port, corresponds to a shaft.

Program usage name

rod_flange

# H — internal temperature
`heat

Details

Heat port related to the temperature of the moist air mixture inside the converter.

Program usage name

thermal_port

# A — humid air inlet
humid air

Details

Humid air port, corresponds to the inverter input.

Program usage name

port

# S — addition or removal of moisture and impurity gases
`moist air

Details

Connect this port to the S port of the unit from the library Moisture & Trace Gas Sources to add or remove moisture and impure gases.

Dependencies

To use this port, set the Moisture and trace gas source parameters to Controlled.

Program usage name

source_port

Output

# mdot_w_out — description missing

Details

Description missing

Data types	Description missing
Complex numbers support	Description missing

# F — vector signal containing data on pressure, temperature, humidity and level of impurity gases
`vector'

Details

An output port that outputs a vector signal. The vector contains the results of pressure (Pa), temperature (K), humidity level and impurity gas level measurements inside the component.

Data types	`Float64`.
Complex numbers support	No

Input

# q — rotation of port R relative to port C, rad
scalar

Details

Input port that transmits position information. Connect this port to the q port of the position sensor.

Dependencies

To use this port, set the parameters Interface rotation to . Provide input signal.

Data types	`Float64`.
Complex numbers support	No

Parameters

Initial Conditions

# Initial trace gas mass fraction — description missing

Details

description missing

Default value	`0.001`
Program usage name	`x_g_start`
Evaluatable	Yes

# Initial relative humidity — description missing

Details

description missing

Default value	`0.5`
Program usage name	`RH_start`
Evaluatable	Yes

Details

description missing

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`T_start`
Evaluatable	Yes

# Initial specific humidity — description missing

Details

description missing

Default value	`0.01`
Program usage name	`x_w_start`
Evaluatable	Yes

Details

description missing

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`287 K`
Program usage name	`T_wb_start`
Evaluatable	Yes

# Initial humidity ratio priority — description missing
None | Low | High

Details

description missing

Values	`None` \| `Low` \| `High`
Default value	`High`
Program usage name	`HR_priority`
Evaluatable	No

# Initial water vapor mole fraction — description missing

Details

description missing

Default value	`0.01`
Program usage name	`y_w_start`
Evaluatable	Yes

# Initial temperature priority — description missing
None | Low | High

Details

description missing

Values	`None` \| `Low` \| `High`
Default value	`High`
Program usage name	`T_priority`
Evaluatable	No

# Initial humidity ratio — description missing

Details

description missing

Default value	`0.01`
Program usage name	`HR_start`
Evaluatable	Yes

# Initial trace gas mole fraction — description missing

Details

description missing

Default value	`0.001`
Program usage name	`y_g_start`
Evaluatable	Yes

# Initial specific humidity priority — description missing
None | Low | High

Details

description missing

Values	`None` \| `Low` \| `High`
Default value	`High`
Program usage name	`x_w_priority`
Evaluatable	No

# Initial mass ratio of water droplets to moist air — description missing

Details

description missing

Default value	`0`
Program usage name	`r_d_start`
Evaluatable	Yes

# Initial trace gas specification — description missing
Mass fraction | Mole fraction

Details

description missing

Values	`Mass fraction` \| `Mole fraction`
Default value	`Mass fraction`
Program usage name	`trace_gas_type`
Evaluatable	No

# Initial pressure priority — description missing
None | Low | High

Details

description missing

Values	`None` \| `Low` \| `High`
Default value	`High`
Program usage name	`p_priority`
Evaluatable	No

# Initial mass ratio of water droplets to moist air priority — description missing
None | Low | High

Details

description missing

Values	`None` \| `Low` \| `High`
Default value	`High`
Program usage name	`r_d_priority`
Evaluatable	No

# Initial trace gas mole fraction priority — description missing
None | Low | High

Details

description missing

Values	`None` \| `Low` \| `High`
Default value	`High`
Program usage name	`y_g_priority`
Evaluatable	No

# Initial wet-bulb temperature priority — description missing
None | Low | High

Details

description missing

Values	`None` \| `Low` \| `High`
Default value	`High`
Program usage name	`T_wb_priority`
Evaluatable	No

# Initial trace gas mass fraction priority — description missing
None | Low | High

Details

description missing

Values	`None` \| `Low` \| `High`
Default value	`High`
Program usage name	`x_g_priority`
Evaluatable	No

# Initial water vapor mole fraction priority — description missing
None | Low | High

Details

description missing

Values	`None` \| `Low` \| `High`
Default value	`High`
Program usage name	`y_w_priority`
Evaluatable	No

# Initial relative humidity priority — description missing
None | Low | High

Details

description missing

Values	`None` \| `Low` \| `High`
Default value	`High`
Program usage name	`RH_priority`
Evaluatable	No

# Initial pressure — description missing
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

description missing

Units	`Pa` \| `uPa` \| `hPa` \| `kPa` \| `MPa` \| `GPa` \| `kgf/m^2` \| `kgf/cm^2` \| `kgf/mm^2` \| `mbar` \| `bar` \| `kbar` \| `atm` \| `ksi` \| `psi` \| `mmHg` \| `inHg`
Default value	`0.101325 MPa`
Program usage name	`p_start`
Evaluatable	Yes

# Initial humidity specification — description missing
Relative humidity | Specific humidity | Mole fraction | Humidity ratio | Wet-bulb temperature

Details

description missing

Values	`Relative humidity` \| `Specific humidity` \| `Mole fraction` \| `Humidity ratio` \| `Wet-bulb temperature`
Default value	`Relative humidity`
Program usage name	`moisture_type`
Evaluatable	No

Moisture and Trace Gas

# Added trace gas temperature specification — method for setting the impurity gas temperature
Atmospheric temperature | Specified temperature

Details

Selection of the impurity gas temperature setting method:

Atmospheric temperature - the atmospheric temperature set by the Moist Air Properties (MA) unit connected to the mains is used.
Specified temperature - the value is set with the parameters Temperature of added trace gas.

Dependencies

To use this parameter, set the Moisture and trace gas source parameters to . Constant.

Values	`Atmospheric temperature` \| `Specified temperature`
Default value	`Atmospheric temperature`
Program usage name	`trace_gas_temperature_type`
Evaluatable	No

Details

description missing

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`T_g_const`
Evaluatable	Yes

# Relative humidity at saturation — description missing

Details

description missing

Default value	`1`
Program usage name	`RH_ws`
Evaluatable	Yes

# Fraction of condensate entrained as water droplets — description missing

Details

description missing

Default value	`1`
Program usage name	`condensate_droplets_fraction`
Evaluatable	Yes

Details

description missing

Units	`kg/s` \| `kg/hr` \| `kg/min` \| `g/hr` \| `g/min` \| `g/s` \| `t/hr` \| `lbm/hr` \| `lbm/min` \| `lbm/s`
Default value	`0 kg/s`
Program usage name	`mdot_moisture_const`
Evaluatable	Yes

Details

description missing

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`T_moisture_const`
Evaluatable	Yes

# Condensation time constant — condensation time constant
s | ns | us | ms | min | hr | d

Details

A time scale factor characterising the time period for the return of the supersaturated volume of moist air to the saturation level due to condensation of excess moisture.

Units	`s` \| `ns` \| `us` \| `ms` \| `min` \| `hr` \| `d`
Default value	`0.001 s`
Program usage name	`condensation_time_constant`
Evaluatable	Yes

Details

description missing

Units	`kg/s` \| `kg/hr` \| `kg/min` \| `g/hr` \| `g/min` \| `g/s` \| `t/hr` \| `lbm/hr` \| `lbm/min` \| `lbm/s`
Default value	`0 kg/s`
Program usage name	`mdot_g_const`
Evaluatable	Yes

# Moisture added or removed — add or remove moisture in the form of water vapour or water
Water vapor | Water droplets

Details

Select whether the unit adds or removes moisture as water vapour or water:

Vapor - the enthalpy of added or removed moisture corresponds to the enthalpy of water vapour, which is greater than the enthalpy of water.
Liquid - the enthalpy of added or removed moisture corresponds to the enthalpy of water, which is less than the enthalpy of water vapour.

Dependencies

To use this parameter, set the parameter Moisture and trace gas source to . Constant.

Values	`Water vapor` \| `Water droplets`
Default value	`Water vapor`
Program usage name	`moisture_source_phase`
Evaluatable	No

# Added moisture temperature specification — Moisture temperature setting method
Atmospheric temperature | Specified temperature

Details

Selects the method for setting the moisture temperature:

Atmospheric temperature - the atmospheric temperature set by the unit Moist Air Properties (MA), connected to the circuit, is used.
Specified temperature - the value is set with the parameters Temperature of added moisture.

Dependencies

To use this parameter, set the Moisture and trace gas source parameters to . Constant.

Values	`Atmospheric temperature` \| `Specified temperature`
Default value	`Atmospheric temperature`
Program usage name	`moisture_temperature_type`
Evaluatable	No

# Water droplets evaporation time constant — description missing
s | ns | us | ms | min | hr | d

Details

description missing

Units	`s` \| `ns` \| `us` \| `ms` \| `min` \| `hr` \| `d`
Default value	`0.001 s`
Program usage name	`evaporation_time_constant`
Evaluatable	Yes

# Moisture and trace gas source — source of moisture and impurity gases
None | Constant | Controlled

Details

This parameter controls the usage of the S port and provides the following options for modelling moisture and impurity gas levels within the unit:

None - no impurity gas is introduced into or extracted from the block. The S port is hidden. This value is used by default.
Constant - moisture and impurity gas are introduced into or extracted from the block at a constant rate. The same parameters as in the Moisture Source (MA) and Trace Gas Source (MA) units are available in the unit settings. The S port is hidden.
Controlled - Moisture and impurity gas are introduced into or removed from the block at a time-varying rate. Port S is open. Units Moisture Source (MA) and Trace Gas Source (MA) are connected to this port.

Values	`None` \| `Constant` \| `Controlled`
Default value	`None`
Program usage name	`moisture_trace_gas_source`
Evaluatable	No

# Water vapor evaporated from liquid or condensed to liquid — description missing

Details

description missing

Default value	`false (switched off)`
Program usage name	`vapor_from_liquid`
Evaluatable	No

Main

# Dead volume — Humid air volume at shaft angle 0
m^3 | um^3 | mm^3 | cm^3 | km^3 | ml | l | gal | igal | in^3 | ft^3 | yd^3 | mi^3

Details

Volume of moist air at shaft angle of rotation equal to 0.

Units	`m^3` \| `um^3` \| `mm^3` \| `cm^3` \| `km^3` \| `ml` \| `l` \| `gal` \| `igal` \| `in^3` \| `ft^3` \| `yd^3` \| `mi^3`
Default value	`1.0e-5 m^3`
Program usage name	`dead_volume`
Evaluatable	Yes

# Environment pressure specification — description missing
Atmospheric pressure | Specified pressure

Details

description missing

Values	`Atmospheric pressure` \| `Specified pressure`
Default value	`Atmospheric pressure`
Program usage name	`pressure_type`
Evaluatable	No

# Environment pressure — description missing
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

description missing

Units	`Pa` \| `uPa` \| `hPa` \| `kPa` \| `MPa` \| `GPa` \| `kgf/m^2` \| `kgf/cm^2` \| `kgf/mm^2` \| `mbar` \| `bar` \| `kbar` \| `atm` \| `ksi` \| `psi` \| `mmHg` \| `inHg`
Default value	`0.101325 MPa`
Program usage name	`p_environment`
Evaluatable	Yes

# Cross-sectional area at port A — area normal to the flow cross-section at the inlet to the transducer
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area of the converter inlet in the direction normal to the wet air flow path.

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`0.01 m^2`
Program usage name	`port_area`
Evaluatable	Yes

Details

Volume of moist air displaced per unit revolution of the shaft.

Units	`m^3/rad` \| `mm^3/rad` \| `cm^3/rad` \| `km^3/rad` \| `m^3/deg` \| `cm^3/rev` \| `m^3/rev` \| `l/rad` \| `l/rev` \| `in^3/rad` \| `ft^3/rad` \| `gal/rad` \| `igal/rad` \| `in^3/deg` \| `in^3/rev` \| `gal/rev`
Default value	`0.01 m^3/rad`
Program usage name	`volume_displacement`
Evaluatable	Yes

# Mechanical orientation — Select the orientation of the inverter
Pressure at A causes positive rotation of R relative to C | Pressure at A causes negative rotation of R relative to C

Details

Select the movement of the shaft in relation to the volume of moist air inside the converter:

Pressure at A causes positive rotation of R relative to C - An increase in the moist air volume results in a positive rotation of port R relative to port C.
Pressure at A causes negative rotation of R relative to C - Increase in the volume of humid air leads to a negative rotation of port R relative to port C.

Values	`Pressure at A causes positive rotation of R relative to C` \| `Pressure at A causes negative rotation of R relative to C`
Default value	`Pressure at A causes positive rotation of R relative to C`
Program usage name	`orientation`
Evaluatable	No

# Initial interface rotation — description missing
rad | deg | rev | mrad | arcsec | arcmin | gon

Details

description missing

Units	`rad` \| `deg` \| `rev` \| `mrad` \| `arcsec` \| `arcmin` \| `gon`
Default value	`0 rad`
Program usage name	`torque_start`
Evaluatable	Yes